Subgroups — C₂×C₅×#14558651 #37558161

Order 23790.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#14558651	C₂	1	1	yes	maximal, characteristic, direct product factor, Hall
2	C₂×C₅×C₁₃×C₆₁	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₂×#14558651	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
4	C₅×C₁₃×C₆₁	C₂×C₃	1	1	yes	characteristic, complemented, Hall
5	#14558651	C₂×C₅	1	1	yes	characteristic, direct product factor, Hall
6	C₂×C₅×C₆₁⋊C₃	—	13	1	no	maximal, Hall
7	C₂×C₁₃×C₆₁	C₃×C₅	1	1	yes	characteristic, complemented, Hall
8	C₅×C₆₁⋊C₃	—	13	1	no	Hall
9	C₁₃×C₆₁	C₂×C₃×C₅	1	1	yes	characteristic, complemented, Hall
10	C₂×C₅×C₆₁	C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
11	C₂×C₅×C₁₃⋊C₃	—	61	1	no	maximal, Hall
12	C₂×C₆₁⋊C₃	—	13	1	no	Hall
13	C₅×C₆₁	C₂×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
14	C₅×C₁₃⋊C₃	—	61	1	no	Hall
15	C₆₁⋊C₃	—	13	1	no	Hall
16	C₂×C₅×C₁₃	C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₆₁	C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Hall
18	C₂×C₁₃⋊C₃	—	61	1	no	Hall
19	C₅×C₁₃	C₂×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
20	C₆₁	C₂×C₅×C₁₃⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₁₃⋊C₃	—	61	1	no	Hall
22	C₂×C₃×C₅	—	793	1	no	Hall
23	C₂×C₁₃	C₅×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Hall
24	C₃×C₅	—	793	1	no	Hall
25	C₁₃	C₂×C₅×C₆₁⋊C₃	1	1	yes	characteristic, complemented, Sylow
26	C₂×C₅	#14558651	1	1	yes	characteristic, direct product factor, Hall
27	C₂×C₃	—	793	1	no	Hall
28	C₅	C₂×#14558651	1	1	yes	characteristic, direct product factor, Sylow
29	C₃	—	793	1	no	Sylow
30	C₂	C₅×#14558651	1	1	yes	characteristic, direct product factor, Sylow

	subgroup	G/H
center, hypercenter	C₂×C₅	#14558651
commutator, cosocle, hypocenter	C₁₃×C₆₁	C₂×C₃×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃×C₆₁	C₃
LCS	G ▷ C₁₃×C₆₁
UCS	C₁ ◁ C₂×C₅

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₅×#14558651	C₂	direct (N × H)
2. C₂×C₅×C₁₃×C₆₁	C₃	semidirect
3. C₂×#14558651	C₅	direct (N × H)
4. C₅×C₁₃×C₆₁	C₂×C₃	semidirect
5. #14558651	C₂×C₅	direct (N × H)
7. C₂×C₁₃×C₆₁	C₃×C₅	semidirect
9. C₁₃×C₆₁	C₂×C₃×C₅	semidirect
10. C₂×C₅×C₆₁	C₁₃⋊C₃	semidirect
13. C₅×C₆₁	C₂×C₁₃⋊C₃	semidirect
16. C₂×C₅×C₁₃	C₆₁⋊C₃	semidirect
17. C₂×C₆₁	C₅×C₁₃⋊C₃	semidirect
19. C₅×C₁₃	C₂×C₆₁⋊C₃	semidirect
20. C₆₁	C₂×C₅×C₁₃⋊C₃	semidirect
23. C₂×C₁₃	C₅×C₆₁⋊C₃	semidirect
25. C₁₃	C₂×C₅×C₆₁⋊C₃	semidirect
26. C₂×C₅	#14558651	direct (N × H)
28. C₅	C₂×#14558651	direct (N × H)
30. C₂	C₅×#14558651	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₅×#14558651	2
C₂×C₅×C₁₃×C₆₁	3
C₂×#14558651	5
C₂×C₅×C₆₁⋊C₃	13
C₂×C₅×C₁₃⋊C₃	61

Subgroups — C2×C5×#14558651 #37558161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₅×#14558651 #37558161